Wavelets, Multiplier spaces and application to Schrödinger type operators with non-smooth potentials

2013/01/04 by Pengtao Li, Li, Pengtao, Qixiang Yang +3
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1301.0696

openalex publication_date 2013/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we employ Meyer wavelets to characterize multiplier spaces between Sobolev spaces without using capacity. Further, we introduce logarithmic Morrey spaces M^t,τ_r,p(ℝⁿ) to establish the inclusion relation between Morrey spaces and multiplier spaces. By wavelet characterization and fractal skills, we construct a counterexample to show that the scope of the index τ of M^t,τ_r,p(ℝⁿ) is sharp. As an application, we consider a Schrödinger type operator with potentials in M^t,τ_r,p(ℝⁿ).

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